Why does Perl not have overloaded functions?

Because you can inspect the argument count, return context, and object types all by yourself.
In Perl, the number of arguments is trivially available to a function via the scalar sense of @_, the return context via wantarray(), and the types of the arguments via ref() if they're references and simple pattern matching like /^\d+$/ otherwise. In languages like C++ where you can't do this, you simply must resort to overloading of functions.